Is it possible to use a 4-pin PWM fan or CPU cooler with a motherboard which has only 3-pin fan headers on it?

Electrically, there is no problem doing this - the fourth pin on the fan cable is used purely for PWM control and is not needed in order for the fan to run. So you can plug the 4-pin fan connector onto the 3-pin motherboard fan header, leaving the fourth pin not connected to anything. The fan will potentially run at full speed, so if you would like to reduce the speed of the fan you will need to adjust the fan speed setting in your BIOS or use fan control software such as SpeedFan in Windows.

The only other problem to consider is that occasionally, components immediately adjacent to the motherboard fan header can get in the way of the larger 4-pin fan connector, physically preventing connection. This problem also occurs if you try to use an in-line fan speed controller such as the one made by Gelid.

Another avenue to explore is the possibility of using a bay-mounted fan controller. Several models are available now which provide 4-pin fan headers, so this is an easy way to use 4-pin PWM fans in a PC system which has only 3-pin fan headers on its motherboards. When using this method, you may find it necessary to disable any fan warning settings in your motherboard BIOS, since the motherboard may incorrectly believe that its CPU fan has failed when the fan is connected to a fan controller rather than directly to the motherboard itself.